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Asymptotic Analysis of Probabilistic Algorithms for Finding Short Codewords

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Eurocode ’92

Part of the book series: International Centre for Mechanical Sciences ((CISM,volume 339))

Résumé

Il a été démontré [1] que le problème de trouver dans un code linéaire binaire un mot de poids donné (en particulier de poids faible) est NP-complet. Ceci permet d’envisager des procédés cryptographiques fondés sur ce fait [5]. Il est donc nécessaire pour assurer la sécurité de tels systèmes d’évaluer les algorithmes existants dont le but est justement de trouver de tels mots. Par exemple, dans [5], trouver l’erreur aléatoire introduite pour chiffrer un mot revient à trouver le mot le plus court d’un code linéaire.

Nous présentons ici l’analyse théorique de deux de ces algorithmes [3, 7]. Ces résultats sont confirmés, tout au moins pour l’un d’eux, par l’implantation, et autorisent des extrapolations pour les grandes dimensions.

Abstract

We present the asymptotic analysis of two algorithms [3, 7] for finding short codewords in linear binary codes. For the first of these algorithms, the results are confirmed by implementation, and this allows extrapolation for larger codes.

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References

  1. E.R. Berlekamp, R.J. McEliece, and H.C.A. Van Tilborg. On the inherent intractability of certain coding problems. IEEE Trans. Inform. Theory, pages 384–386, 1978.

    Google Scholar 

  2. P.J. Lee and E.F. Brickell. An observation on the security of McEliece’s public-key cryptosystem. In Advances in Cryptology - EUROCRYPT ‘88, pages 275–280. Lecture Notes in Computer Science, Springer 1989. 330.

    Google Scholar 

  3. J.S. Leon. A probabilistic algorithm for computing minimum weights of large error-correcting codes. IEEE Trans. Inform. Theory, IT-34(5): 1354–1359, September 1988.

    Google Scholar 

  4. F.J. MacWilliams and N.J.A. Sloane. The Theory of Error-correcting Codes. Nord- Holland, 1983.

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  5. R.J. McEliece. A public-key cryptosystem based on algebraic coding theory. DSN progress report, 42–4, 1978.

    Google Scholar 

  6. J.N. Pierce. Limit distribution of the minimum distance of random linear codes. IEEE Trans. Inform. Theory, IT-13(17): 595–599, 1967.

    Google Scholar 

  7. J. Stern. A method for finding codewords of small weight. In Coding Theory and Applications, pages 106–113. Lecture Notes in Computer Science, Springer 1989. 388.

    Google Scholar 

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Author information

Authors and Affiliations

  1. Ecole Normale Supérieure, Paris, France

    F. Chabaud

  2. Ecole Polytechnique, 91128, Palaiseau Cedex, France

    F. Chabaud

Authors
  1. F. Chabaud
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Editor information

Editors and Affiliations

  1. INRIA — Rocquencourt, France

    P. Camion  & P. Charpin  & 

  2. University of Toulon and Var — La Garde, France

    S. Harari

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© 1993 Springer-Verlag Wien

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Chabaud, F. (1993). Asymptotic Analysis of Probabilistic Algorithms for Finding Short Codewords. In: Camion, P., Charpin, P., Harari, S. (eds) Eurocode ’92. International Centre for Mechanical Sciences, vol 339. Springer, Vienna. https://doi.org/10.1007/978-3-7091-2786-5_15

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  • DOI: https://doi.org/10.1007/978-3-7091-2786-5_15

  • Publisher Name: Springer, Vienna

  • Print ISBN: 978-3-211-82519-8

  • Online ISBN: 978-3-7091-2786-5

  • eBook Packages: Springer Book Archive

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